1. Field of the Invention
The present invention generally relates to the measurement of electrical characteristics of formations surrounding a wellbore. More particularly, the present invention relates to a method for determining horizontal and vertical resistivities in anisotropic formations.
2. Description of Related Art
It is well known that subterranean formations surrounding an earth borehole may be anisotropic with regard to the conduction of electrical currents. The phenomenon of electrical anisotropy is generally a consequence of either microscopic or macroscopic geometry, or a combination thereof, as follows.
Many subterranean formations include sedimentary strata in which electrical current flows more easily in a direction parallel to the bedding planes, as opposed to a direction perpendicular to the bedding planes. One reason is that a great number of mineral crystals possess a flat or elongated shape (e.g., mica or kaolin). At the time they were laid down, they naturally took on an orientation parallel to the plane of sedimentation. The interstices in the formations are, therefore, generally parallel to the bedding plane, and the current is able to easily travel along these interstices which often contain electrically conductive mineralized water. Such electrical anisotropy, sometimes called microscopic anisotropy, is observed mostly in shales.
Many subterranean formations also include a series of relatively thin beds having different lithological characteristics and, therefore different resistivities. In well logging systems, the distances between the electrodes or antennas are great enough that the volume involved in a measurement may include several such thin beds. When individual layers are neither delineated nor resolved by a logging tool, the tool responds to the formation as if it were a macroscopically anisotropic formation. A thinly laminated sand/shale sequence is a particularly important example of a macroscopically anisotropic formation.
If a sample is cut from a subterranean formation, the resistivity of the sample measured with current flowing parallel to the bedding planes is called the transverse or horizontal resistivity xcfx81h. The inverse of xcfx81h is the horizontal conductivity "sgr"h. The resistivity of the sample measured with a current flowing perpendicular to the bedding plane is called the longitudinal or vertical resistivity, xcfx81v, and its inverse the vertical conductivity "sgr"V. The uniaxial anisotropy coefficient xcex is defined as: xcex={square root over ("sgr"h/"sgr"v.)}
In some formations, there is an added complication, in that even for currents flowing parallel to the bedding plane, the conductivity varies with direction. This situation is termed xe2x80x9cbiaxial anisotropyxe2x80x9d, and it is characterized by three different conductivity values along each of three different axes. The conductivity for currents flowing along the z-axis (i.e., perpendicular z, while the conductivity for currents flowing along the x axis (i.e., x. The conductivity for y. The biaxial anisotropy coefficients xcexxz, xcexyz are defined as xcexxz={square root over ("sgr"x/"sgr"z,)}xcexyz={square root over ("sgr"y/"sgr"z.)}
In situations where the borehole intersects the formation substantially perpendicular to the bedding planes, conventional resistivity logging tools are sensitive almost exclusively to the horizontal component of the formation resistivity. For induction tools, this is a consequence of the induced currents flowing in horizontal planes. For Galvanic devices, the lack of sensitivity to anisotropy is even more stringent due to the xe2x80x9cparadox of anisotropyxe2x80x9d, which states that any array of electrodes or sensors deployed along the axis of a wellbore in a vertical well is insensitive to the vertical component of resistivity, despite the intuitive expectation to the contrary.
A number of non-Galvanic logging tools have been designed to detect uniaxial anisotropy. See, for example, U.S. Pat. No. 4,302,722, issued Nov. 24, 1981. Such tools are unable to measure biaxial anisotropy, and in addition, they are ineffective in non-conductive, oil-based drilling muds. A tool that can function in such environments, and which could measure biaxial anisotropy, would be desirable.
Accordingly, there is disclosed herein a logging tool that can measure the resistive anisotropy of formations around a borehole. In one embodiment, the system comprises a logging tool coupled to a surface unit. The logging tool includes a set of electrodes that contact a wall of the borehole, with the set of electrodes including a first pair of current electrodes spaced apart vertically, and a second pair of current electrodes spaced apart horizontally. Between the first pair of current electrodes is two or more measurement electrodes that measure a vertical axis voltage difference caused by a current flowing between the first pair of current electrodes. Similarly, two or more measurement electrodes between the second pair of current electrodes measure a horizontal axis voltage difference caused by a current flowing between the second pair of current electrodes. A resistive anisotropy can be calculated from the measured voltage differences. A third pair of current electrodes oriented perpendicularly with respect to the first and second pair of current electrodes may be provided. Measurement electrodes between the third pair of current electrodes may be used to measure a third voltage difference that may be used with the other voltage differences to measure the biaxial resistive anisotropy of the formation. The anisotropy calculations are preferably performed by the surface unit after it receives measurements from the logging tool.